Identification of clusters of companies in stock indices via Potts super-paramagnetic transitions

The clustering of companies within a specific stock market index is studied by means of super-paramagnetic transitions of an appropriate q-state Potts model where the spins correspond to companies and the interactions are fun ctions of the correlation coefficients determined from the time dependence of the companies' individual stock prices. The method is a generalization o f the clustering algorithm by Domany ct al. to the case of anti-ferromagnet ic interactions corresponding to anti-correlations. For the Dow Jones indus trial average where no anti-correlations were observed in the investigated time period, the previous results obtained by different tools were well rep roduced. For the Standard & Poor's 500, where anti-correlations occur, repu lsion between stocks modify the cluster structure. (C) 2000 Elsevier Scienc e B.V. All rights reserved.